Field Effect Transistors for Terahertz Detection: Physics and ... - arXiv

Field Effect Transistors for Terahertz Detection: Physics and First Imaging Applications W. Knap, M. Dyakonov, D. Coquillat, F. Teppe, N. Dyakonova Université Montpellier2 - CNRS, Place E. Bataillon, 34950 Montpellier, France

J. Łusakowski, K. Karpierz, M. Sakowicz Institute of Experimental Physics, University of Warsaw, ul. Hoża 69, 00-681 Warsaw, Poland

G. Valusis, D. Seliuta, I. Kasalynas Semiconductor Physics Institute, A. Gostauto 11, LT-01108 Vilnius, Lithuania

A. El Fatimy, Y.Meziani, T. Otsuji Tohoku University RIEC Ultra-broadband Signal Processing 2-1-1 Katahira, Aoba-ku 980-8577 Japan

Abstract: Resonant frequencies of the two-dimensional plasma in FETs increase with the reduction of the channel dimensions and can reach the THz range for sub-micron gate lengths. Nonlinear properties of the electron plasma in the transistor channel can be used for the detection and mixing of THz frequencies. At cryogenic temperatures resonant and gate voltage tunable detection related to plasma waves resonances, is observed. At room temperature, when plasma oscillations are overdamped, the FET can operate as an efficient broadband THz detector. We present the main theoretical and experimental results on THz detection by FETs in the context of their possible application for THz imaging. 1. Introduction The channel of a field effect transistor (FET) can act as a resonator for plasma waves. The plasma frequency of this resonator depends on its dimensions and for gate lengths of a micron and sub-micron (nanometer) size can reach the terahertz (THz) range. The interest in the applications of FETs for THz spectroscopy started at the beginning of ‘90s with the pioneering theoretical work of Dyakonov and Shur [1] who predicted that a steady current flow in a FET channel can become unstable against generation of the plasma waves. These waves can, in turn, lead to the emission of the electromagnetic radiation at the plasma wave frequency. This work was followed by the another one where the same authors have shown that the nonlinear properties of the 2D plasma in the transistor channel can be used for detection and mixing of THz radiation [2]. It is worth noting that this work treated rigorously and gave a complete description of the resonant as well as the non-resonant (overdamped) plasma oscillation regimes.

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THz emission in the nW power range from submicron GaAs and GaN FETs has been observed both at cryogenic as well as at room temperatures [3-5]. At the moment, however, FET based THz microsources can not compete with existing Quantum Cascade Lasers (QCL) or Time Domain Spectroscopy (TDS) sources in the practical applications. It appeared, nevertheless, that THz detection by FETs can be very promising and close to applications. Here we present an overview of the recent results on detection obtained in different types of III-V semiconductor-based nanometer-sized High Electron Mobility Transistors (HEMTs) [6-12]. Many experimental results were obtained at cryogenic temperatures where the resonant plasma modes can be excited [8, 9, 11, 12]. However, already in the first experiments, it was shown that GaAs/AlGaAs and GaInAs/GaAs HEMTs can also operate as THz broadband detectors at room temperatures [6, 7, 9]. From the application point of view research on Si-MOSFETs was very important. It has been demonstrated that Si-MOSFETs can be efficient room temperature detectors of sub-THz radiation and can be used up to 2.5 THz as well [13, 14]. Their noise equivalent power was found to be one of the lowest of all room temperature operating fast THz detectors [14]. They have been recently integrated in focal plane arrays and checked for imaging applications [15, 16]. The main well established facts about THz detection by FETs are: i) the resonant detection observed at cryogenic temperatures is due to plasma waves related rectification and ii) at room temperature the plasma wave oscillations are overdamped but the rectification mechanism is still efficient and enables a broadband THz detection and imaging. The paper is organized as follows. Section 2 describes the basic principles of the detection with FETs. Section 3 presents an overview of the main experimental results on sub-THz and THz detection. Recent results on plasma resonance narrowing by geometrical factors and the drain current are also presented therein. Section 4 gives practical examples concerning THz imaging. 2. Principles of terahertz detection by FETs The idea of using a FET for emission and detection of THz radiation was put forward by Dyakonov and Shur [1, 2]. The possibility of the detection is due to nonlinear properties of the transistor, which lead to the rectification of an ac current induced by the incoming radiation. As a result, a photoresponse appears in the form of dc voltage between source and drain which is proportional to the radiation power (photovoltaic effect). Obviously, some asymmetry between the source and drain is needed to induce such a voltage. There may be various reasons of such an asymmetry. One of them is the difference in the source and drain boundary conditions due to some external (parasitic) capacitances. Another one is the asymmetry in feeding the incoming radiation, which can be achieved either by using a special antenna, or by an asymmetric design of the source and drain contact pads. Thus the radiation may predominantly create an ac voltage between the source and the gate (or between the drain and the gate) pair of contacts. Finally, the asymmetry can naturally arise if a dc

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current is passed between source and drain, creating a depletion of the electron density on the drain side of the channel [3]. In most of the experiments carried out so far, the THz radiation was applied to the transistor channel, together with contact pads and bonding wires. In such a case, it is obviously difficult to define how exactly the radiation is coupled to the transistor. Important experimental information about the way of coupling to a real device was obtained from experiments with polarized subTHz radiation [17, 18] and with focused THz radiation [19]. These results are presented in Sect. 3. Theoretically, we will consider the case of an extreme asymmetry, where the incoming radiation creates an ac voltage with amplitude Ua only between the source and the gate, see Fig. 1. We will also assume that there is no dc current between the source and drain.

Fig. 1. Schematics of a FET as a THz detector (above) and the equivalent circuit (below).

Generally, the FET may be described by an equivalent circuit presented in Fig. 1. The obvious elements are the distributed gate-to-channel capacitance and the channel resistance, which depends on the gate voltage through the electron concentration in the channel: en = CU,

(1)

where e is the elementary charge, n is the electron concentration in the channel, C is the gate-to-channel capacitance per unit area, and U is the gate to channel voltage. Note, that Eq. 1 is valid locally, so as long as the scale of the spatial variation of U(x) is larger than the gate-to-channel separation (the gradual channel approximation). Under static conditions and in the absence of the drain current, U = U0 = Vg - Vth, where U0 is the voltage swing, Vg is the gate voltage, and Vth is the threshold voltage at which the channel is completely depleted. The inductances in Fig. 1 represent so called kinetic inductances, which are due to the electron inertia and are proportional to m, the electron effective mass. Depending on the frequency ω, one can distinguish two regimes of operation, and each of them can be further divided into two subregimes depending on the gate length L.

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1. High frequency regime occurs when ωτ > 1, where τ is the electron momentum relaxation time, determining the conductivity in the channel σ = ne2τ/m. In this case, the kinetic inductances in Fig. 1 are of primordial importance, and the plasma waves analogous to the waves in an RLC transmission line, will be excited. The plasma waves have a velocity s=(eU/m)1/2 [1] and a damping time τ. Thus their propagation distance is sτ. 1a. Short gate, L< sτ. The plasma wave reaches the drain side of the channel, gets reflected, and forms a standing wave with an enhanced amplitude, so that the channel serves as a resonator for plasma oscillations. The fundamental mode has the frequency ~ s/L, with a numerical coefficient depending on the boundary conditions. 1b. Long gate, L>>sτ. The plasma waves excited at the source will decay before reaching the drain, so that the ac current will exist only in a small part of the channel adjacent to the source. 2. Low frequency regime, ωτ >1, and the induced ac current will leak to the gate at a small distance l from the source, such that the resistance R(l) and the capacitance C(l) of this piece of the transistor channel satisfy the condition ωτRC(l) = 1, where τRC(l) = R(l)C(l) = l2ρC. This condition gives the value of the "leakage length" l on the order of (ρCω) –1/2 (which can also be rewritten as s(τ/ω)1/2). If l1, and s(τ/ω)1/2 for ωτ 1), where plasma oscillations are excited (the case 1b). There is however some quantitative differences, see Eq. 2 below. Anyway, plasma waves are excited and their existence in this case has been clearly confirmed by the recent detection experiments in the magnetic fields [23]. The plasma waves cannot propagate above the cyclotron frequency. Therefore, in experiments with a fixed radiation frequency the photoresponse is strongly reduced when the magnetic field goes through the cyclotron resonance. This is probably the most spectacular manifestation of the importance of plasma waves in the terahertz detection by FETs [23]. Mechanism of the nonlinearity. The most important mechanism is the modulation of the electron concentration in the channel, and hence of the channel resistance, by the local ac gate-to-channel voltage, as described by Eq. 1. Because of this, in the expression for the electric current j = env, both the concentration, n and the drift velocity, v will be modulated at the radiation frequency. As a result, a dc current will appear: jDC = e, where n1(t) and v1(t) are the modulated components of n and v, and the angular brackets denote averaging over the oscillation period 2π/ω. Under open circuit conditions a compensating dc electric field will arise, resulting in the photoinduced source-drain voltage ∆U. A simplified theory. The most important case is that of a long gate (the regimes 1b and 2b) when, independently of the value of the parameter ωτ, the ac current excited by the incoming radiation at the source cannot reach the drain side of the channel. For this case within the hydrodynamic approach the following result for the photoinduced voltage was derived [2]:  U a2  2ωτ  ∆U = 1+ . (2) 2  4U 0  1 + (ωτ )  

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As seen from this formula, the photoresponse changes only by a factor of 3, as the parameter ωτ increases from low to high values, even though the physics becomes different: at ωτ>1 plasma waves are excited, while at ωτ